Recall that a persistent data structure allows access to previous versions while supporting updates. How can you leverage this property in a BST to maintain multiple versions efficiently?

The potential method requires defining a potential function that captures the "cost" of future operations. Consider how the structure of a BST changes with insertions/deletions and how this affects potential.

For a persistent BST, each update creates a new version. How might you model the potential function to account for the cumulative cost of maintaining all versions, especially when paths diverge or merge?